After you obtain HMs, you should have Pokémon that know Cut, Fly, Strength, and Surf with you at all times. Flash is only required in the Rock Tunnel.

Catch a Caterpie in Viridian Forest, train it to level 17 so it learns Sleep Powder, and use it to catch a level 8 Abra. This Abra, once evolved into a Kadabra, will be a very powerful Pokémon that can easily solo the rest of the game.

Defeat every trainer before moving on to another area, as you may not be able to battle some trainers after certain conditions are met.

It is better to catch or defeat the west Snorlax first:

The east Snorlax can be partially bypassed by using Surf.

The west Snorlax blocks the entrance to the top of Route 16, which goes downhill towards Fuchsia city. Going uphill is a lot slower, so having easy access to the top is more convenient.

Since training Pokémon makes them stronger than wild Pokémon of the same level, it is best to trade for NPC Pokémon using the lowest level Pokémon possible.

The Pay Day move can be used to gain unlimited money:

Blue version can catch a Meowth, which learns Pay Day at level 17.

Red version can use TM16 to teach Pay Day to a suitable Pokémon.

Your Bicycle should be the top item in your inventory. You can deposit items that are above it to move it up.